Optimal diluent allocation in production systems with diluent-ESP-lifted wells

(1)

Optimal diluent allocation in production systems with diluent-ESP-lifted wells

Ruben Dario Ensalzado

Natural Gas Technology

Supervisor: Truls Gundersen, EPT Co-supervisor: Milan Stanko, IPT

Department of Energy and Process Engineering Submission date: June 2016

Norwegian University of Science and Technology

(2)

(3)

(4)

(5)

(6)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 1

OPTIMAL DILUENT ALLOCATION IN PRODUCTION SYSTEMS WITH ESP-LIFTED WELLS Rubén Ensalzado¹ ([email protected])

Under supervision of: Truls Gundersen¹ ([email protected]) and Milan Stanko² ([email protected])

1Department of Energy and Process Engineering; Norwegian University of Science and Technology; Trondheim, Norway

2Department of Petroleum Engineering and Applied Geophysics; Norwegian University of Science and Technology; Trondheim, Norway

Summary

In this research, the author presents the development of a numerical model for production systems (wells and surface flowlines) to determine optimal diluent allocation. The model includes the main inflow performance equations to represent reservoir deliverability, pressure and temperature drop calculations in tubing, electric submersible pump (ESP) modeling including viscosity and frequency correction equations, and oil blending models for the injection module. For the injection module, both ASTM D7152-11 standard and Cragoe (1933) methods are available. For the production fluid modeling, the author considered the black oil model to calculate thermodynamic properties and an emulsion model to calculate fluid viscosity depending on its water cut. The gas phase was neglected. The model was developed by using object-oriented programming (OOP) in a commercial software.

1. Introduction

According to the U.S. Energy Information Administration (U.S. Energy Information Administration, 2014), the world expects a growth in demand for oil within the next 25 years, due to the emerging economies of China, India and the Middle East. Between 2010 reported value, and 2040 projections, these countries expect a moderate growth in demand, from 40,0 mn BPD to almost 75,0 mn BPD. In global terms, it is also expected to have a growth rate of 3,2% between these next 25 years, with a liquid oil consumption reaching a peak of 108,0 mn BPD by the end of 2040.

This would represent a big challenge to oil producing companies, considering the current economic scenario, where profits out of the business have reduced significantly since the 2014.

Lower oil & gas prices have been a recurrent topic in annual reports of most oil companies. Statoil (Statoil, 2016) indicated that 2015 was a year of very volatile prices, ranging from USD 66 to USD 35 between May and December, for the reference Brent crude oil.

These figures affected the company performance, including significant layoff during last year. BP reported a loss of USD 6.5 bn comparing with the expected results based on 2014 prices (BP, 2016).

With these falling revenues, the British company stated that operational cost and activities have to be re-based, and they expect 2016 and the following

years to be a period of intense change with ongoing restructuring. Saudi Aramco (Saudi Aramco, 2016) also anticipates the upcoming years to be volatile in terms of oil prices, requiring more smart investments based on a solid risk management framework, and reducing uncertainties in every step of the way.

Based on this philosophy, the Saudi state-owned company has reported a steady increase in their oil production since 2011 to 2015, from 9,1 to 10,2 mn BPD.

It is clear that players in the oil market have keep up the pace to this VUCA world we are living in now. Oil companies have the challenge to satisfy this growing demand while dealing with lower prices, especially considering the current depletion of what is known as conventional reservoirs.

Having better understanding about this challenge, it is helpful to have a glance to the characteristics of the current oil reserves around the world. In the following graphs, there is an overview of the oil proved reserve distribution up to the end of 2014.

According to BP, (BP, 2015) the total number to date is 1,7 bn barrels.

(7)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 2 Figure 1. Oil proved reserves up to the end 2014, by

region (BP, 2015).

Proved reserves is concept with different meanings for the industry, especially when it comes to its quantification. However, generally speaking it refers to the quantified oil reservoirs available in the world that, with the known technology, expertise and economic conditions, can be recovered at a reasonable return rate (BP, 2015).

As expected, not every barrel of the reported reserves is from the same type. The following plot depicts these oil reserves based on a density classification.

Figure 2. Oil proved reserves up to the end 2014, by type.

The terms light, medium, heavy and extra heavy oil refer to the high density of those oils. As an indicator of crude density, the industry uses API gravity. This unit is inversely proportional to the density or the specific gravity of an oil: the higher the API gravity, the lighter the crude oil and vice versa. As a reference, water API gravity at standard conditions is 10. There is no fixed line between each category

about an oil’s “heaviness”, but the following rules are well accepted:

 Light oil: 32-40 °API

 Medium oil: 32-25 °API

 Heavy oil: 25-10 °API

 Extra-heavy oil: <10 °API

Bitumen is an additional classification, with an API grade lower than 10 API, but with additional consideration about its viscosity.

From the operational point of view, heavy oil, extra- heavy oil and bitumen are considered unconventional resources, since companies will have to invest more in its production, when compared to light and medium oil reservoirs.

Coming back to Figure 2, this means that out of these 1,7 bn barrels, roughly 38% constitutes conventional reserves, and the remaining 62% is unconventional oil. With a R/P ratio of 52 years, oil companies are driven to develop soon new tools and technologies to commercially develop more unconventional reservoirs, which in previous years were not that attractive.

In terms of location, between Canada and Venezuela, they gather around 30-35% of these unconventional resources. However, these American countries are not the only ones that have to be prepared to manage these type of crude oils. In the UK continental shelf, Mariner field is a typical case in Europe. According to Statoil, who holds 65% of its production licenses, Mariner has been subject to a number of development studies by various operators, since its discovery in 1981. However, feasibility studies from then indicated that it was not economically possible to develop it. In 2012, Statoil made the investment decision and the production is expected to commence in 2018 with an average plateau production of 55.000 BPD with total reserves up to 250 mn barrels.

Risk management is the key to drive smarter investments into the business, and the real asset in this project and portfolio management discipline is information. With high-quality data and tools for scenario analysis, it is possible to quantify risks and make decisions for developing new and already existing fields. Mariner field is a sample of this fact.

To reduce the risk, in recent years, virtually every company in the business has invested in developing computational tools for evaluating scenarios, training

13,7%

19,4%

47,7% 9,1%

7,6%

2,5%

Oil: Total proved reserves 2014

Total North America Total S. & Cent.

America Total Europe &

Eurasia Total Middle East Total Africa Total Asia Pacific

25,3%

38,3%

36,5%

Oil: Reserve classification 2014

Heavy and Extra Heavy Bitumen Light and Medium

(8)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 3 staff, undergoing feasibility studies, and trying to

anticipate to technical challenges before proceeding to operations.

More and better tools have to be developed to help companies with their investment plans in fields that were not considered before. Having more than a billion oil barrels in these kind of reserves should be a good incentive to go in that direction.

With this background, the present study intends to provide tools to analyze a particular technique usually applied to heavy and extra-heavy oil reservoirs: diluent injection. The main objective was to develop a physically accurate and flexible model to study this technique, particularly for production systems with ESP-lifted wells. Among its features, the model should allow performing optimization to allocate an optimal diluent injection rate for single wells and networks.

As per the author’s opinion, this particular topic has a promising outlook, but very little has been written about it. New tools to show this technique’s performance have to be developed now and fast.

This work is a step forward into this direction.

1.1. Problem description

For heavy and extra-heavy oil fields there is often a critical operational problem: oil viscosity. As a general case, oil found on these type of reservoirs has a high viscosity. The more viscous the fluid, the more energy and pressure losses along the production infrastructure. In order to overcome this problem, these fields are often developed with wells equipped with electric submersible pumps (ESP) to lift the pressure of the fluid to the surface. Another way to approach this challenge is to include diluent injection lines at various levels of the well (completion or along the tubing) to reduce the in-situ viscosity, hence reducing the pressure losses. When combined, these two IOR techniques are very promising, since the diluent injection may reduce the power requirement of the ESP and improve its performance.

Diluent injection is not a new term to the industry when it comes to heavy and extra-heavy oil recovery.

Since 1999, there are references at SPE journals describing the potential of diluent injection to reduce the in-situ viscosity of these low-gravity oils, increasing the lifting capabilities and ultimately oil

recovery. Garnett and Dee (Garnett & Dee, 1999) presented the results from a pilot test in the US including an implementation of light-oil injection in a heavy oil reservoir. They indicated that the oil average recovery increased 50 times using this technique. Rojas (Rojas, 2001) presented results on a new application in Venezuela for bitumen recovery (~8,5 °API) using diluent injection directly at the well completion. For this case study, the oil in-situ viscosity was 5.000 cP, at reservoir conditions (58 °C and 8100 kPa). More recently, in 2010, Brito, Garcia and Brown (Brito, Garcia, & Brown, 2010) presented results on an implementation of diluent and gas injection for the same purpose. This implementation is a step forward to the diluent injection technology, which is already considered traditional in Venezuela.

As an interesting fact, they mentioned that in one of the production areas of oil state-own company PDVSA, a total of 343 wells have a diluent-injection implementation, with a combined production of 55.000 BPD. Maintenance for these injection facilities represent a major part of their operational expenditures, therefore they focused on another alternative different that an ESP for diluent injection.

Despite being a standard practice on those countries, there is no information available about whether the diluent injection rate could be optimal or not for a given production system. In gas lifting, gas injection to the well improve the production of a well due to the reduction of density, and consequently reduction on the potential losses in the fluid column. However, after certain injection rate, the additional material added in the system increases the hydraulic losses due to friction (Golan & Whitson, 1996). A similar behavior is expected in diluent injection.

Using diluent injection as an IOR technique also has some operational challenges: availability of diluent on site, capital investment on the infrastructure required, operational expenditure due to diluent injection facilities, among others. Therefore, allocating in advance an optimal diluent injection and performance curves describing its behavior for oil production systems is of great importance to the industry.

Diluent injection is not available in most commercial simulators related to oil production. In its last version, PROSPER® (13.0) from PETEX included this capability with a limited set of oil blending options.

Another widely used simulator PIPESIM® for Schlumberger, in its version 2012.2 included diluent

(9)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 4 and gas injection directly over vertical tubing, but

again, with limited capability in terms of blending method and location of the injection point over the well infrastructure. Considering this, most evaluations related to diluent injection are currently running over in-house applications or spreadsheets, difficult to scale up or to use in different scenarios.

This fact reduces the risk management and planning capabilities of companies willing to implement this technique in their current assets. Additional to this, it does not provide a platform susceptible to optimization and feasibility analysis in a plain implementation.

As a sample of this issue, some data used as background of this study, includes a development from a software company that coupled different software to produce diluent injection performance curves. During this development several workarounds were made to modelled effectively diluent injection with the existing commercial software.

Therefore, this study attempts to provide an implementation of a physically accurate production model, in which diluent injection can be easily implemented for feasibility studies and economic evaluations.

1.2. Objectives

The main objective of the study was to develop a comprehensive and physically accurate model to represent both single wells and networks, including the following capabilities:

 Using ESP as a fluid lifting method, including as input equipment performance curves and working with affinity laws for centrifugal pumps for correcting performance due to changes on rotational speed.

 Working with viscous fluids, including the required correction factors to the appropriate elements of well infrastructure.

 Using injection points in any part of the well infrastructure (not only completion or tubing), including different methods for crude blending and property calculation.

 Susceptible to optimization using separable and non-separable functions.

As additional specific objectives, the following are included:

 Performing sensitivity analysis on the diluent injection performance of single well infrastructures with respect to the following variables: pump rotational speed, reservoir water cut, and wellhead pressure.

 Implementing optimization techniques in the models developed. In particular, applying separable and non-separable objective function optimization for a case study production network. In this context, separable objective functions refer to the production of individual wells which behavior is independent from other wells, and non-separable objective functions consider that there is dependency between the wells.

2. Nomenclature 2.1. Acronyms bn Billion, 10⁹ BPD Barrels per day

ESP Electric submersible pump IPR Inflow performance relationship IOR Improved oil recovery

mn Million, 10⁶. O/W Oil in Water

OOP Object-oriented programming R/P Reserves-to-production USD US dollars

VBA Visual basic for applications

VUCA Volatile-Uncertain-Complex-Ambiguous W/O Water in Oil

2.2. Greek letters 𝛾 Specific gravity 𝜌 Phase density 𝜃 Pipe inclination angle 𝜇 Phase viscosity 2.3. Symbols

𝐵 Phase volumetric factor

(10)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 5 𝐶𝑝 Phase specific heat

𝑑_𝑖 Pipe internal diameter 𝑓𝑑 Darcy friction factor

𝑔 Gravity acceleration 𝑚̇ Mass flow rate

𝑝 Pressure 𝑅_𝑠 Gas in oil ratio

𝑞̇ Volumetric flow rate 𝑇 Temperature 𝑢 Phase velocity

𝑈𝑖 Overall heat coefficient, internal 𝑊𝐶 Water cut

𝑦 Vertical axis/direction 2.1. Subscripts

𝑤 Water phase

𝑜 Oil phase

𝑔 Gas phase

𝑒 Emulsion

∞ Surroundings or environment

𝑠𝑐 Standard conditions 3. Model fundamentals

In Petroleum Engineering, a production system is a set of elements that allow producing oil and gas from a reservoir. Production systems include both wells and surface networks, typically grouped in what the industry qualifies as upstream. These elements can be modelled by a set of mechanical and thermodynamic equations to reproduce how they affect the phase behavior along its path to the surface. Figure 3 provides a simplified sketch from a single well, part of the production systems modelled in this study.

Figure 3. Simplified representation of a single well infrastructure.

Highlighting its elements, the well typically consists of the following elements:

 Vertical completion

 Tubing

 ESP

 Diluent injection point

For developing the production system model, the main governing equations for each element were included. Therefore, no special treatment about mechanical design details was made, e.g., the model does not include material specifications and limitations, system geometry, centrifugal pump operational details (cavitation or erosion due to solids, for example), among others.

In the following sections, there is a complete description of these equations and how they were applied to the element’s model.

3.1. Fluid model

To predict the phase behavior for a broad range of crude oils using minimum inputs, the black oil model was selected. For a complete thermodynamic description of the model, a review to (Whitson &

Brulé, 2000) is advised. This model was conceived for upstream applications, where typically only operational variables are available, e.g., pressure and temperature.

This model considers three different pseudo fluids characterized by the production fluid phases: gas, oil

Single Well Infrastructure

Produced fluids (Black oil model)

Tubing section

Electro submersible pump (centrifugal)

Diluent injection point Tubing section Vertical completion

(11)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 6 and water. A set of properties quantitatively describe

the mass transfer between the phases, but essentially the model indicates that all phases are different substances. This is applicable for water and hydrocarbon-based phases, but between gas and liquid oil, this is not true. However, for all practical purposes and typical operating ranges for the industry, this model is well-accepted for describing phase behavior.

Black oil model properties are:

 Gas, oil and water volume factor (Bg, Bo, Bw).

 Solution gas oil ratio (Rs).

 Gas-oil ratio (GOR).

 Compressibility factor (Co).

 Bubble point pressure (Pb).

These properties are dependent of the surface operations used as reference, therefore, the model allows to include tuning factors to adjust the property values to the experimental data. In this way, different crude oil properties can be described using the same correlations. Details on correlations used for each property can be found on this study’s appendixes.

Although properties of the gas phase are computed in the model, the gas flowrate is neglected in all relevant calculations.

Additional to these properties, the black oil model was used to calculate local flow rates for all phases, based on flow rates at standard conditions. The transformation matrix for this calculation is given by Equation 1.

[ 𝑞_𝑔̇ 𝑞_𝑜̇ 𝑞_𝑤̇

] = [

𝐵_𝑔 −𝐵_𝑔∙ 𝑅_𝑠 0

0 𝐵_𝑜 0

0 0 𝐵_𝑤

] ∙ [ 𝑞𝑔,𝑠𝑐̇ 𝑞𝑜,𝑠𝑐̇ 𝑞_{𝑤,𝑠𝑐}̇

] (1)

The same approach is used to calculate the phases densities. The transformation matrix for this calculation is shown in Equation 2.

[ 𝜌𝑔

𝜌_𝑜 𝜌𝑤

] = [

1/𝐵𝑔 0 0

𝑅𝑠/𝐵𝑜 1/𝐵𝑜 0

0 0 1/𝐵_𝑤

] ∙ [ 𝜌_{𝑔,𝑠𝑐} 𝜌𝑜,𝑠𝑐

𝜌_{𝑤,𝑠𝑐}] (2) For computing the viscosity of the oil and water mixture, an emulsion model was used. W/O and O/W emulsions are easily formed on production systems, due to the presence of both phases in virtually all fields.

W/O and O/W emulsions properties have been studied thoroughly by the industry, including characterization of their behavior, developing correlations for calculation and implementation of techniques to modify them in a favorable manner.

The following bullet points summarize the factor of interests for this study related to W/O and O/W emulsions behavior.

 The viscosity of a W/O emulsion is generally higher than the value of its oil phase at the same operating/experimental conditions (Duan, Jiaqiang, Jinzhu, Xiaofeng, &

Xiaoguang, 2010).

 As water cut increases, W/O emulsion viscosity increases as well, for a given pressure and temperature.

 There is an inversion point at which the emulsion regime changes from W/O to O/W.

This inversion point is given within a water cut range of 60%-80% (Rønningsen, 1995).

 After the inversion point, the emulsion viscosity drops suddenly. Depending on the sample, this drop may reach several orders of magnitude.

To illustrate these facts, Figure 4 depicts data of an extra-heavy oil sample, with an inversion point relative to the water cut of 60%.

Figure 4. Viscosity behavior of a hydrocarbon-water emulsion in terms of production water cut (%).

To compute the viscosity, the Richardson model was used. Using this model, the viscosity is calculated by using Equation 3.

𝜇_𝑒= 𝜇_𝑜∙ 𝑒^𝐴∙^𝑊𝐶¹⁰⁰^, 𝑊𝐶 < 𝐶 (3a) 𝜇𝑒= 𝜇𝑤∙ 𝑒^𝐵∙¹⁰⁰^𝑊𝐶^, 𝑊𝐶 > 𝐶 (3b)

0,0 200,0 400,0 600,0 800,0 1000,0 1200,0 1400,0 1600,0

0,0 20,0 40,0 60,0 80,0 100,0

Emulsion viscosity [cP]

Water cut [%]

W/O and O/W emulsion viscosity behavior

W/O emulsion O/W emulsion

(12)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 7 As per the constants A, B, and C, 3,215; 3,089; and

60% were used respectively (Stanko, 2014). To perform calculations with the model, the user has to provide these constants.

3.2. Piping model

In a single well infrastructure, tubing hydraulic losses and energy balances can be modeled as a traditional piping. Also, this model can be used for horizontal and inclined flowlines, since the same physical laws apply.

The following premises were considered to develop these models:

 Single phase flow along the pipe. The fluid model considers two different phases, water and oil, however, for these calculations a pseudo-homogeneous fluid is used, taken a mass average on the thermodynamic properties and using an effective viscosity for transport calculations.

 Using effective viscosity to calculate friction losses. The effective viscosity is defined as the oil-water emulsion viscosity, which will depend on the dominant phase.

 Using weight fraction of the phases (water and oil) to calculate heat capacity and density at each discretization point.

 Using Darcy definition for the friction factor calculation.

 Considering constant mass flow rate along the piping sections. So, in case there is an injection point, the calculation is performed before or after that point.

 Discretizing control volumes to solve the differential equations using finite differences and implementing linear equation solvers.

This operation is required since the fluid properties change with temperature and pressure. Therefore, this discretization provides a more accurate calculation of them, along the pipe.

As mentioned, hydraulic losses were calculated using the simplified momentum equation in one dimension, for a homogenous fluid. Equation 4 refers to the formulation for the tubing, but is valid to horizontal and inclined flowlines.

−𝑑𝑝(𝑦)

𝑑𝑦 = 𝜌(𝑦) ∙ 𝑔 ∙ 𝑐𝑜𝑠(𝜃) + 𝑓_𝑑𝜌(𝑦) ∙ 𝑢(𝑦)² 2 ∙ 𝑑_𝑖 (4) For energy balances along the pipe, a general approximation of heat transfer mechanisms was made. In this way, in case the temperature of the fluid is higher than the temperature of the surroundings, the heat from the fluid is transferred to the pipe internal wall by convection, along its thickness by conduction and then, depending on the well infrastructure alternating convection and conduction for in its annular region, casing, cementing, and finally the surrounding soil. To reduce this complexity, an overall heat transfer coefficient has to be provided to solve the model.

The general energy balance for a vertical tubing, rearranged as a suitable finite differences expression, is given by Equation 5.

−𝑑𝑇(𝑦)

𝑑𝑦 =𝑑_𝑖∙ 𝑈_𝑖∙ (𝑇(𝑦) − 𝑇_∞)

𝑚̇ ∙ 𝐶𝑝(𝑦) (5)

This expression is also valid for horizontal and inclined flowlines.

For the case of vertical tubing inside the well, no special consideration is being made about the casing and all layers affecting the heat conduction radially, the heat transfer coefficient is referred to the internal diameter of the tubing. As for flowlines, a similar approach is considered.

3.3. ESP model

As common industry definition an electric submersible pump, or ESP for short, is a vertical centrifugal pump with multiple stages, designed to be installed inside a well. Therefore, two group of equations to describe the performance of centrifugal pumps were used.

The first group was centrifugal pump affinity laws.

These so-called laws allow calculating the performance of a pump, from a reference performance curve. These set of equations relate the following variables:

 Rotational speed

 Head

 Capacity

 Impeller diameter

 Power consumption

(13)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 8 The typical performance curves of a centrifugal pump

include:

 Head-capacity curves

 Power-capacity curves

The capacity is expressed in terms of volume units per time unit, head is expressed in distance units, and power in terms of energy per time unit.

The second group of equations is related to performance correction due to viscosity of the fluid.

Fluid viscosity affects the performance of centrifugal pumps, since they depend on developing kinetic energy due to rotation and then converting this energy into pressure in the pump’s volute. The more viscous the fluid, the more frictional losses in the inter blade passages and pump impeller.

Typically, pump manufacturers provide the performance curves using water as a reference fluid (γw = 1), so users can adapt them according to their needs. For completing this correction, the procedure suggested by the American Hydraulic Institute (ANSI/HI Standard 9.6.7, 2010) was used, suitable for centrifugal pumps and viscous liquids up to 4.000 cSt.

Figure 5. Viscosity effect on centrifugal pumps performance.

In the Figure 5 is depicted the pump performance at two different values of fluid viscosity. Figure 6 depicts the pump performance correcting by both viscosity effect and reduced rotational speed.

Figure 6. Viscosity and reduced speed effect on centrifugal pump performance.

3.4. Blending model

Oil blending is required in the injection points and in the mixing nodes of a network to compute the new oil properties, such as viscosity, density, and heat capacity. Using these values, new black oil properties are calculated.

For this purpose, two main methods were included in the model: ASTM D7152 (ASTM Standard D7152, 2011) and Cragoe (Cragoe, 1933). Sæten (Sæten, 2014) provided a study case comparing these two methods using North Sea crude oils, particularly from Mariner field. The results for both methods were satisfactory in terms of predicting viscosity values (kinematic or absolute); furthermore, the author suggested that ASTM D7152 method provided a lower deviation with the experimental data available.

3.5. IPR models

The model included five (5) different IPR calculation methods:

 Productivity index

 Jones equation

 Fetkovich equation

 Back pressure equation

 Vogel equation

As a reference formulation about those particular IPR calculation methods, equations given in (Beggs, 2003) were used.

Every model included both variants: oil and gas production. In the current version of the model, the gas phase is neglected, however, the model supports an expansion to gas wells in further research.

0 200 400 600 800 1000 1200 1400

0 100 200 300 400 500 600 700 800

Pump head [m]

Pump capacity [m3/h]

Viscosity effect on pump performance

Pump performance @ ν = 1 cSt Pump performance @ ν = 400 cSt

0 200 400 600 800 1000 1200 1400

0 100 200 300 400 500 600 700 800

Pump head [m]

Pump capacity [m3/h]

Viscosity and reduced speed effect on pump performance

Pump performance @ ν = 1 cSt, Nc = 3600 rpm Pump performance @ ν = 400 cSt, Nc = 3000 rpm

(14)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 9 4. Methodology

As mentioned before, the main objective of this study was to provide a comprehensive and physically accurate model to evaluation diluent injection and ESP-lifting technologies in single wells and networks.

Efforts completed during this semester attempted to continue previous work from the Specialization Project (Ensalzado, 2015), including system integration for single well infrastructure, development of network infrastructure, sensitivity analysis, and optimization.

In the following sections, a more detailed insight about the study development is given.

4.1. Quality management

In order to guarantee that the model provides an accurate representation of physical elements, an extensive quality management phase was deployed.

The main topics revised were as follows:

 Viscosity blending accuracy.

 Tubing hydraulic and temperature profiles

 ESP performance

 Black oil property calculation accuracy.

This quality verification was done against two commercial simulators, PIPESIM (version 2012.2) and PROSPER (version 13.0). During the testing, some programming bugs were detected and corrected, but in general terms, the results presented a small deviation within the range of 3%-5% from the aforementioned simulators.

Several factors may explain this deviation, however the differences in the tuning factor programming for the black oil properties seemed to be the most relevant of them. Despite the deviation, the results showed the expected uncertainty and were satisfactory to proceed to the next phase.

4.2. Model development

The model was developed completely in MATLAB (R2015a) using OOP. There is a detailed explanation about the classes capabilities in Section 5.

The low level objects were programmed during the previous semester, so during this period the focus was made in the two integration classes:

SingleWellObj and NodeObj. These classes provide

the rules for interaction between the low level elements and the model functionality.

4.3. Literature revision

Since most of the literature review related to the governing laws of the model was completed during the fall semester 2015; the main focus during this period was on optimization and programing techniques applicable for the implementation.

The topics revised were as follows:

 Linear programming, including implementation of special-ordered sets (SOS).

 Non-linear optimization theory for convex problems.

 Implementation of optimization in MATLAB, for both linear programming and non-linear systems.

 Advanced programming techniques in Object-oriented languages, applicable to MATLAB, including event handling.

4.4. Peer-to-peer presentations

During the development period, two relevant peer-to- peer presentations were made.

The first one, at the Department of Petroleum Engineering and Applied Geophysics (IPT) Spring PhD Seminars 2016. For this seminar a poster with the main highlights of the research up to date was presented and discussed with peers attending the session. As mentioned before, this particular is a traditional practice in the American continent, but it represents a novelty in developments on the North Sea fields.

The second presentation was done to Petroleum Cybernetics, a group developed by the Department of Technical Cybernetics (ITK) and IPT. During the presentation, the details about the model development were presented and discussed, with particular emphasis on the challenges related to the implementation of optimization techniques.

4.5. Reporting

In order to guarantee that the users can use and extend the model capabilities a set of additional documents were developed. These documents focus

(15)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 10 on the programming details of the classes including

the following topics:

 Properties

 Methods

 Main algorithms of solving

Special emphasis was made on the black oil class (BOObj) and viscosity adjustment and calculation.

As for the first topic, there are several correlations and calculation routines available for computing the black oil model properties. Because of that, an additional report including the correlations and validity ranges was prepared.

In regard to the viscosity adjustment and calculation, something similar was developed. Using experimental data from oil field, a series of validations were made. The results were included in an additional technical report.

5. Programming approach

As mention on the study briefing, OOP was used as the programming technique for developing the model. There are many advantages using this approach for model development, including the following:

 Extensibility. It is possible to add system’s elements to the model with minimum, if any, modification to the existing classes.

 Encapsulation. Procedures, algorithms and correlation for model operation are included in the classes, so the user has no exposure to its logic of execution.

 Modularity. The system can be developed in independent modules. Also, instances of these modules can be executed independently from each other.

Most commercial software for petroleum and process engineering support some kind of OOP, especially for customization. For example, PIPESIM® has the package called OpenLink® which allows interacting with external applications such as MS Excel through VBA. RESOLVE® from PETEX also provide this capability, using MS Excel as an interphase to calculate and report variables. PIPEPHASE® from Schneider Electric (former Invensys) also supports extensibility with OOP software or languages.

OOP is based on classes. They can be seen as the template that defines properties, methods and events

for a particular object. An object is an instance of a class, i.e., a populated variable based on the class.

For describing the model, eight classes were developed:

 BOObj class

 InjectionObj class

 TubingObj class

 FlowlineObj class

 VertCompletionObj class

 ESPObj class

 SingleWellObj class

 NodeObj class

An important remark about the development of these classes is that they all belong to the super class type handle. In MATLAB, there are two different super classes types: handles and values. The main difference between them is that every object created from a handle-type class is passed as a reference to any other instance: therefore, the changes made in any moment will be reflected automatically in every instance in which the object is used. In an object created from a value-type class, an independent copy is given to other instances so the changes are applied locally.

The next sections include a description about the classes hierarchy and main features of each of them.

5.1. Object hierarchy

Classes can have different levels of interaction, so it is convenient to define hierarchies among them. In this way, low level classes can be used to build more complex and specific ones.

In this particular case, for the model developed, a two-level hierarchy was considered. First-level classes are independent building blocks, that require different type of data and run independently from any other. Second-level classes are dependent on first- level classes to operate. This hierarchy is shown in Figure 7.

(16)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 11 Figure 7. Classes Hierarchy levels.

The second-level classes depend on the first level- classes as shown in the following diagrams.

Figure 8. Class dependency: NodeObj class.

Figure 9. Class dependency: SingleWellObj class.

Figure 10. Class dependency: TubingObj class.

Figure 11. Class dependency: FlowlineObj class.

5.2. BOObj class

This class contains all correlations for property calculation and adjustment algorithms related to the black oil model.

The main function of the class is calculating black oil properties of a given fluid. As mentioned, every second-level class requires a BOObj instance as an input.

The minimum information required by an object from this class is as follows:

 Pressure.

 Temperature.

 Oil specific gravity.

 Gas specific gravity.

 Water specific gravity.

 Oil viscosity reference matrix (two values at different temperature levels, at standard pressure).

5.3. ESPObj class

This class contains all expressions and correlations to describe an ESP performance. It includes:

 Outlet pressure.

 Viscosity adjustment using the ANSI/HI 9.6.7 standard (ANSI/HI Standard 9.6.7, 2010). As suggested by the standard, the maximum viscosity value is 4.000 cSt.

 Adjustment of pump performance due to actual impeller rotational speed using affinity laws.

 Adjustment of pump power consumption for a given impeller rotational speed, using affinity laws.

TubingObj

Second level classes First level classes

FlowlineObj

SingleWellObj

NodeObj

BOObj

ESPObj

VertCompletionObj

InjectionObj

NodeObj BOObj

Required Only once

InjectionObj Required Only once

SingleWellObj Required Multiple times

FlowlineObj Required Multiple times

NodeObj Optional Multiple times

SingleWellObj VertCompletionObj

Required Only once

BOObj Required Only once

TubingObj Optional Multiple times

ESPObj Optional Multiple times

InjectionObj Optional Multiple times

TubingObj BOObj

Required Only once

FlowlineObj BOObj

Required Only once

(17)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 12 The minimum information required by an object from

this class is as follows:

 Head-capacity performance curve, for a reference fluid (water).

 Reference impeller rotational speed.

 Actual impeller rotational speed.

 Pump best efficiency point (BEP).

5.4. FlowlineObj class

This class contains all expressions to model a horizontal pipeline. This class is very similar to the TubingObj, but it was specially designed to interact with SinglewellObj and NodeObj classes. The energy losses calculation is based on a constant value for the ambient temperature. It allows to perform the following calculations:

 Hydraulic losses due to friction.

 Thermal energy balances.

 Forward and backward calculation.

 Pressure and temperature profiles, given in charts or in plots.

 Black oil model defined by the BOObj class.

 Internal diameter.

 Pipeline roughness.

 Length.

 Ambient temperature.

 Overall heat transfer coefficient.

 Pressure (at one end).

 Temperature (at one end).

 Phases’ flowrates (at one end, at actual conditions).

 Phases’ flowrates (at one end, at standard conditions).

 Phases’ density values (at standard conditions).

5.5. InjectionObj class

This class allows to calculate the properties of an oil blending. As discussed in section 3.4, it applies two different procedures for that: ASTM D7152-11 and Cragoe’s.

As a main output, it provides a new reference viscosity matrix for a given blend, to be used in a BOObj object for tuning.

 Diluent flowrate.

 Diluent density.

 Diluent viscosity reference matrix (two values at different temperature levels, at standard pressure).

 Oil flowrate.

 Oil density.

 Injection/blending temperature.

5.6. TubingObj class

This class contains all expressions to model a buried vertical pipeline. This class is very similar to the FlowlineObj, but it was designed to be included as part of SingleWellObj class items. One important different with the FlowlineObj class is that energy losses calculation is based on the geothermal profile instead of a constant ambient temperature.

It allows to perform the following calculations:

 Hydraulic losses due to friction.

 Thermal energy balances.

 Ascending and descending calculation.

 Pressure and temperature profiles, given in charts or in plots.

 Internal diameter.

 Pipeline roughness.

 Length.

 Geothermal temperature gradient.

 Overall heat transfer coefficient.

 Pressure (at one extrema).

 Temperature (at one extrema).

 Phases’ flowrates (at one extrema, at actual conditions).

 Phases’ flowrates (at one extrema, at standard conditions).

5.7. VertCompletionObj class

This class provides all correlations to compute a well’s IPR. As described in section 3.5, it is possible to use up to 5 methods for gas and oil wells, providing the appropriate parameters for each model.:

(18)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 13 The minimum information required by an object from

this class is as follows:

 IPR type.

 Selected IPR parameters.

 Reservoir pressure.

 Reservoir temperature.

5.8. SingleWellObj class

This class is an integration structure. It allows to solve a single well object, identifying every item included and interconnecting them with each other.

After that, it applies a solving algorithm to calculate the bottom hole pressure, estimating the well flowrate.

 Wellhead pressure.

 Well building items. As a minimum requirement, at least a VertCompletionObj object has to be included. Other items may include TubingObj, ESPObj and InjectionObj objects.

5.9. NodeObj class

This class is an integration structure. It allows to solve a set of branches and nodes, given a fixed pressure. It applies a solving algorithm to calculate wellhead pressures for SingleWellObj objects and node pressures for NodeObj objects.

 Node pressure.

 Branches or nodes, or both. For the case of branches, a combination of a SingleWellObj object and a FlowlineObj,object must be given. For nodes, a combination of a NodeObj and a FlowlineObj object must be provided as input.

6. Sensitivity analysis

The objective of this analysis was to compute the diluent performance curves of a given single well infrastructure and determine its sensitivity with multiple operational variables.

As a base case for performing the study an artificial well example was created. This well included two tubing sections, an ESP, and one diluent injection line. More details could be found on the appendixes section 12.1.

The variables included in this analysis were pump’s impeller rotational speed (Nc), reservoir water cut (%) and wellhead pressure (Pwh). For each variable, four (4) plots were given Variables ranged as follow:

 Pump’s impeller rotational speed: from 2800 rpm to 3600 rpm.

 Reservoir water cut: from 0% to 70%.

 Wellhead pressure: from 40 bara to 90 bara.

The results are depicted in Figures

0 500 1000 1500 2000 2500 3000 3500 4000

0 100 200 300 400 500 600 700 800 900

Oil resevoir rate, qo [Sm3/d]

Diluent injection, qd [Sm3/d]

WC 0% @ Pwh = 60 bara

Nc = 2800 rpm Nc = 3000 rpm Nc = 3200 rpm Nc = 3400 rpm

0 500 1000 1500 2000 2500 3000 3500 4000

0 100 200 300 400 500 600 700 800 900

WC 20% @ Pwh = 60 bara

(19)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 14 Figure 12. Sensitivity analysis: reservoir water cut effect on diluent injection performance.

Figure 13. Sensitivity analysis: impeller rotational speed effect on diluent injection performance.

0 500 1000 1500 2000 2500 3000 3500 4000

0 100 200 300 400 500 600 700 800 900

WC 40% @ Pwh = 60 bara Nc = 2800 rpm

0 500 1000 1500 2000 2500 3000 3500 4000

0 100 200 300 400 500 600 700 800 900

WC 70% @ Pwh = 60 bara Nc = 3000 rpm

Nc = 3200 rpm Nc = 3400 rpm Nc = 3600 rpm

0 500 1000 1500 2000 2500 3000 3500 4000

0 100 200 300 400 500 600 700 800 900

Nc 3600rpm @ Pwh = 60 bara

WC = 70%

WC = 60%

WC = 40%

WC = 20%

0 500 1000 1500 2000 2500 3000 3500 4000

0 100 200 300 400 500 600 700 800 900

WC = 70%

WC = 60%

WC = 40%

WC = 20%

0 500 1000 1500 2000 2500 3000 3500 4000

0 100 200 300 400 500 600 700 800 900

WC = 70%

WC = 60%

WC = 40%

WC = 20% 0

500 1000 1500 2000 2500 3000 3500 4000

0 100 200 300 400 500 600 700 800 900

WC = 70%

WC = 60%

WC = 40%

WC = 20%

0 500 1000 1500 2000 2500 3000 3500

0 100 200 300 400 500 600 700 800 900

Nc 3600rpm @ WC = 0 %

Pwh = 90bara Pwh = 80 bara Pwh = 70 bara Pwh = 60 bara Pwh = 50 bara

0 500 1000 1500 2000 2500 3000 3500

0 100 200 300 400 500 600 700 800 900

Nc 3600rpm @ WC = 20 %

Pwh = 90 bara Pwh = 80 bara Pwh = 70 bara Pwh = 60 bara Pwh = 50 bara

(20)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 15 Figure 14. Sensitivity analysis: wellhead pressure effect on diluent injection performance.

After performing the analysis, it was possible to reach the following conclusions:

 Diluent injection improves oil recovery, as long as the liquid phase behaves as a W/O emulsion. For these cases, there is an optimal diluent injection rate.

 Diluent injection does not improve oil recovery when the liquid phase behaves as a O/W emulsion. In all cases tested, diluent injection decreased the oil recovery rate.

 Oil production rate is proportional to the impeller rotational speed of the ESP.

Therefore, the higher the rotational speed of the pump, the higher the energy transfer rate to the fluid, hence, the higher the head developed by the fluid.

 Oil production decreases as the reservoir water cut increases. This observation is valid as long the water cut does not reach the inversion point, i.e., the liquid phase behaves as a W/O emulsion. After the inversion point, due to the change of emulsion regime, the production may increase as shown in Figure 13.

 Oil production rate is inversely proportional to the wellhead pressure, as expected. An interesting observation was that the optimal diluent rate did not show an apparent change with the wellhead pressure; therefore, once the optimal is found for a given wellhead pressure, it provides a good approximation of the optimal for other values.

7. Optimization

As mentioned in the study’s objectives, after developing the numerical model, two different optimization applying two schemes: separable and non-separable functions.

In optimization, separable objective functions refer to elements of a system or network with no interactions.

Therefore, the changes on separable function variable will not affect the remaining targets.

Consequently, it is possible to run every system element independently from each other. In Petroleum Production Engineering, this case may represent satellite wells which do not share a cluster or with no interconnection between one and other. Using this approach, the optimization implementation can be run separately from the system; certainly a computational advantage, since it is possible to collect all data from the system performance in a prior stage and later use the information for optimization.

On the other hand, non-separable objective functions refer to elements with mutual dependency, therefore, the performance of one element will affect the remaining elements of the system. In this case, it is not possible to run independently elements from the system. In oil production, it may represent systems with multiple wells interconnected by a cluster, manifold or branch. From the optimization perspective, the optimizer has to run on top of the model application, and requires information from the system at every step. From the computational point of view, it is also more resource demanding than the separable objective function approach.

0 500 1000 1500 2000 2500 3000 3500

0 100 200 300 400 500 600 700 800 900

Nc 3600rpm @ WC = 40 %

0 500 1000 1500 2000 2500 3000 3500

0 100 200 300 400 500 600 700 800 900

Nc 3600rpm @ WC = 60 %

(21)

Norwegian University of Science and Technology TEP4905 – Industrial Process Engineering Master Thesis 16 Despite their differences, these two approaches are

of interest of the industry since they represent different real cases; hence, the model developed must be capable to answer to both requirements.

For this study case, the objective function subject to optimization was the reservoir oil production for both individual wells and the network, and the optimization variables were the diluent injection rates in each of the wells. As a reference of the computational performance, all cases were tested in a personal computer with an Intel Core i5-3337U @ 1.80 GHz processor and with 12,0 GB of RAM.

In the following sections there is a complete explanation of these two implementation including computational performance details.

7.1. Separable objective functions

As mentioned before, in the context of this study, separable objective functions refer to the oil production of different single wells with no interconnection. In this way, the performance of each well does not affect the others.

For this approach, a set of artificial wells (up to 100) were modelled. With the well architectures defined, diluent performance curves for each well were computed, ranging the diluent injection rate from 0 to 900 m³/d. The curves were as shown in Figures 12 to 14. A sample of these curves is available in the appendixes’ section 12.3.

In order to optimized this set of data, a mathematical expression depending on the diluent injection rate and resulting in the reservoir oil production must be developed. For doing this, two particular function types were selected: piecewise linear functions and polynomials.

In optimization, using these two types of functions provides different advantages:

 With piecewise linear functions, linear programming optimization techniques can be used. This reduces the complexity of the implementation, dealing only with linear equation systems. The challenge in this case is the optimization problem formulation.

 With polynomials, the gradient and hessian matrices are easily obtained, therefore, optimization algorithms based on them converge efficiently.

7.2. Piecewise linear modelling

As stated in the previous section, the main challenge using piecewise linear modelling is the optimization problem formulation. For this purpose, several options were considered, including using special ordered sets (SOS). In SOS formulation a certain number of optimization variables from a given set can be different than zero. This is a very usual approach in optimization applications in Economics.

However, it was possible to implement a simpler approach, which allowed using a traditional linear programming solver. The model is described by Equation 6.

𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒: 𝑓(𝑥) = ∑ ∑ 𝑠_𝑗𝑘𝑥_𝑗𝑘

𝑟𝑗

𝑘=1 𝑛

𝑗=1

(6a) 0 ≤ 𝑥_𝑗𝑘 ≤ 𝑑_𝑘− 𝑑_𝑘−1 (6b) 𝑘 = 1, … , 𝑟𝑗 < 𝑗 = 1, … , 𝑛 (6c) In this equation, the indexes j and k refer to the number of objective functions (number of independent well in this case) and the number of segments for each function respectively. The variable sjk refers to the k^th segment slope of the j^th function; the variable xjk refers to the diluent injection rate for the k^th segment of the j^th function, and the variables dk and dk-1 represent the boundaries of the optimization variable xjk. More details of the formulation can be review in (Jensen & Bard, 2003).

For the study, the number of wells was ranged from 10 to 100 and the number of segments from 5 to 10.

Additional to this, different proportions of diluent injection were considered; once the unconstrained diluent rate was obtained, the following cases were run using 80%, 60% and 40% of this unconstrained rate. The purpose of this was to determine if additional restrictions to the model had an impact on the optimization performance.

For optimizing the model, the MATLAB® built-in function linprog was used. More information about this function can be found in (The MathWorks, Inc., 2016).

The results from these optimization cases and the running time are available on the appendixes’ section 12.3.

From the cases tested, there are some worth mentioning observations: